Question

The nearest star to Earth is Proxima Centauri, 4.3 light-years away.

Answer 1

Answer:

a) v = 2,152 10⁸ m / s   b)   t = 2.71 10⁸ s  or t =  85.93 year

Explanation:

a) In this special relativity exercise we have that time is measured in the same ship, so it is the proper time,

    v = d / t

Let's reduce the distance to the SI system

    d = 4.3 l and (9.46 1015 m / 1ly) = 40.678 10¹⁵ m

    t = 5.0 y (365 day / 1 y) (24 h / 1 day) (3600s / 1h) = 1.89 10⁸ s

Let's calculate

    v = 40.678 10¹⁵ / 1.89 10⁸

    v = 2,152 10⁸ m / s

b) The time seen from the ground for which the ship moves is given by

     t = t₀ / √ (1- (v/c)²)

Let's calculate

     t = 1.89 10⁸ / √ (1 - (2.152 / 2.998)²)

     t = 1.89 10⁸ / 0.6962

     t = 2.71 10⁸ s

Let's reduce this time to years

    t = 2.71 10⁸ s (1h / 3600s) (1day / 24h) (1 and / 365 d)

    t =  85.93 year